Depth-Guided Disocclusion Inpainting of Synthesized RGB-D Images.

We propose to tackle the problem of RGB-D image disocclusion inpainting when synthesizing new views of a scene by changing its viewpoint. Indeed, such a process creates holes both in depth and color images. First, we propose a novel algorithm to perform depth-map disocclusion inpainting. Our intuitive approach works particularly well for recovering the lost structures of the objects and to inpaint the depth-map in a geometrically plausible manner. Then, we propose a depth-guided patch-based inpainting method to fill-in the color image. Depth information coming from the reconstructed depth-map is added to each key step of the classical patch-based algorithm from Criminisi et al. in an intuitive manner. Relevant comparisons to the state-of-the-art inpainting methods for the disocclusion inpainting of both depth and color images are provided and illustrate the effectiveness of our proposed algorithms.

Exemplar-based inpainting: technical review and new heuristics for better geometric reconstructions.

This paper proposes a technical review of exemplar-based inpainting approaches with a particular focus on greedy methods. Several comparative and illustrative experiments are provided to deeply explore and enlighten these methods, and to have a better understanding on the state-of-the-art improvements of these approaches. From this analysis, three improvements over Criminisi et al. algorithm are then presented and detailed: 1) a tensor-based data term for a better selection of pixel candidates to fill in; 2) a fast patch lookup strategy to ensure a better global coherence of the reconstruction; and 3) a novel fast anisotropic spatial blending algorithm that reduces typical block artifacts using tensor models. Relevant comparisons with the state-of-the-art inpainting methods are provided that exhibit the effectiveness of our contributions.

Recent advances in diffusion MRI modeling: Angular and radial reconstruction.

Recent advances in diffusion magnetic resonance image (dMRI) modeling have led to the development of several state of the art methods for reconstructing the diffusion signal. These methods allow for distinct features to be computed, which in turn reflect properties of fibrous tissue in the brain and in other organs. A practical consideration is that to choose among these approaches requires very specialized knowledge. In order to bridge the gap between theory and practice in dMRI reconstruction and analysis we present a detailed review of the dMRI modeling literature. We place an emphasis on the mathematical and algorithmic underpinnings of the subject, categorizing existing methods according to how they treat the angular and radial sampling of the diffusion signal. We describe the features that can be computed with each method and discuss its advantages and limitations. We also provide a detailed bibliography to guide the reader.

Efficient and robust computation of PDF features from diffusion MR signal.

We present a method for the estimation of various features of the tissue micro-architecture using the diffusion magnetic resonance imaging. The considered features are designed from the displacement probability density function (PDF). The estimation is based on two steps: first the approximation of the signal by a series expansion made of Gaussian-Laguerre and Spherical Harmonics functions; followed by a projection on a finite dimensional space. Besides, we propose to tackle the problem of the robustness to Rician noise corrupting in-vivo acquisitions. Our feature estimation is expressed as a variational minimization process leading to a variational framework which is robust to noise. This approach is very flexible regarding the number of samples and enables the computation of a large set of various features of the local tissues structure. We demonstrate the effectiveness of the method with results on both synthetic phantom and real MR datasets acquired in a clinical time-frame.

Evaluation of q-space sampling strategies for the diffusion magnetic resonance imaging.

We address the problem of efficient sampling of the diffusion space for the Diffusion Magnetic Resonance Imaging (dMRI) modality. While recent scanner improvements enable the acquisition of more and more detailed images, it is still unclear which q-space sampling strategy gives the best performance. We evaluate several q-space sampling distributions by an approach based on the approximation of the MR signal by a series expansion of Spherical Harmonics and Laguerre-Gaussian functions. With the help of synthetic experiments, we identify a subset of sampling distributions which leads to the best reconstructed data.

Efficient computation of PDF-based characteristics from diffusion MR signal.

We present a general method for the computation of PDF-based characteristics of the tissue micro-architecture in MR imaging. The approach relies on the approximation of the MR signal by a series expansion based on Spherical Harmonics and Laguerre-Gaussian functions, followed by a simple projection step that is efficiently done in a finite dimensional space. The resulting algorithm is generic, flexible and is able to compute a large set of useful characteristics of the local tissues structure. We illustrate the effectiveness of this approach by showing results on synthetic and real MR datasets acquired in a clinical time-frame.

Variational, geometric, and statistical methods for modeling brain anatomy and function.

We survey the recent activities of the Odyssée Laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function. We start with the problem of reconstructing sources in MEG and EEG, and discuss the variational approach we have developed for solving these inverse problems. This motivates the need for geometric models of the head. We present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance (MR) images. Anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but, in the current state of the technology, it must be preceded by a robust estimation and regularization stage. We discuss our work based on variational principles and show how the results can be used to track fibers in the white matter (WM) as geodesics in some Riemannian space. We then go to the statistical modeling of functional magnetic resonance imaging (fMRI) signals from the viewpoint of their decomposition in a pseudo-deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory. Multimodal image matching is discussed next in the framework of image statistics and partial differential equations (PDEs) with an eye on registering fMRI to the anatomy. The paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases.